Vanessa is 3 times as old as Brandon. Ten years ago, Vanessa was 8 times as old as Brandon. How old is Brandon now?
Solution: We can use the given information to write down two equations that describe the ages of Vanessa and Brandon. Let Vanessa's current age be $v$ and Brandon's current age be $b$ The information in the first sentence can be expressed in the following equation: $v = 3b$ Ten years ago, Vanessa was $v - 10$ years old, and Brandon was $b - 10$ years old. The information in the second sentence can be expressed in the following equation: $v - 10 = 8(b - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $v$ and substitute it into our second equation. Our first equation is: $v = 3b$ . Substituting this into our second equation, we get: $3b$ $-$ $10 = 8(b - 10)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $3 b - 10 = 8 b - 80$ Solving for $b$ , we get: $5 b = 70.$ $b = 14$.